In the Lurgi process where coal is gasified, there are tar oil by-products comprising o-cresol, p-cresol, m-cresol, o-ethylphenol, 2,6-xylenol, 2,4-xylenol, and 3,5-xylenol. While the cresols are valuable, the tar acids are discarded because of the difficulty of separating the cresols from the o-ethylphenol and 2,6-xylenol. Since they have the same approximate boiling point they can't be separated by distillation.
Similarly, the oil industry extracts phenolics with caustic but is not able to separate the phenols from one another.